Polyphonic tone synthesizers which utilize digital data to generate musical tones are well known. U.S. Pat. No. 3,515,792, for example, describes a digital organ in which waveshape data is stored in memory and is used to generate one or more musical notes of predetermined waveshape at fundamental frequencies determined by the keys selected on a keyboard. The digital data is converted to an audio signal by a digital-to-analog converter. Another tone synthesizer using digital information to provide a computer organ is described in U.S. Pat. No. 3,809,786 in which the digital data defining the waveform of the desired sound is computed in real time in response to operation of one or more keys on a keyboard. Again the digital data is converted to an audio signal by a digital-to-analog converter system. In copending application Ser. No. 603,776, filed Aug. 11, 1975, entitled "Polyphonic Tone Synthesizer" there is described a synthesizer having a plurality of separate tone generators. Each tone generator includes a Shift register for storing waveform data, the data being shifted out at a rate controlled by a Note clock, the frequency of the Note clock being determined by the particular key selected on a keyboard. The data transferred out of the shift register is applied to a digital-to-analog converter to generate the corresponding audio signal of the desired waveform. In each of these systems, the digital-to-analog converter includes a sample and hold circuit commonly referred to as a zero-order sample and hold, or sometimes referred to as a "boxcar" detector. Digital numbers are converted to analog voltages applied to the sound system by converting each digital number to an analog voltage whose instantaneous amplitude is directly determined by the magnitude of the digital number. A sample and hold circuit then maintains the voltage level at the output until the next digital number in sequence can be converted to its corresponding voltage.
It is characteristic of such a digital conversion system, in which the data occurs at periodic intervals, that the spectral components are imaged at all integer multiples of the periodic interval. In the case of the digital-to-analog converter, this periodic interval is the period at which successive conversions are made is frequently referred to as the sampling period.
The effectiveness of a zero-order sample and hold circuit as an extrapolating device for the digital-to-analog conversion depends upon the sampling frequency in relation to the highest frequency term in the spectral content of the digital data sequence. In general, the higher the sampling frequency in comparison to the highest frequency term in the digital data sequence, the more effective is the suppression of unwanted harmonic components. In the digital tone generators of the type described in the above-identified patents, the sampling frequency for the digital-to-analog converter was selected to be higher than the minimum effective sampling rate for the highest frequency harmonic. In the systems described, the fundamental frequency of the highest note C.sub.7 is f.sub.C7 = 2093 hz. The sampling frequency f.sub.s then was made in excess of 2 .times. 16 .times. 2093 = 66.976 KHZ, which is twice the frequency of the 16th harmonic of the highest note on the keyboard. Considering the case in which the note C.sub.2 having a frequency of 65.4 hz. is played, there is negligible attenuation of the fundamental frequency by the zero-order sample and hold circuit. At the image frequency f.sub.s -f.sub.C2, the zero-order sample and hold circuit should theoretically provide an attenuation of -60.2 db for the image signal.
However, in the case of the tone generators such as described in the above-identified patents, there are fixed number of sample points per cycle of the tone being generated, e.g., 32 distinct sample points per cycle of the audio signal being generated. Thus the effective sampling frequency is limited in such case to 32 times the fundamental frequency of the tone beong generated. Therefore, even though the digital-to-analog converter samples the data at a much higher frequency, no additional information is derived by the higher sampling rate, since successive samplings by the converter simply repeat the same points.
Since the effective sampling rate is only 32 times the fundamental, the image frequency for C.sub.2 is only 2027:62 and the zero-order sample and hold provides a theoretical attenuation of only -29.8 db. While this would appear to be a substantial level of attenuation, the sensitivity of the human ear is much greater at the image frequency of 2027.6 hz than at the fundamental frequency of 65.4 hertz. The curves of equal loudness as a function of frequency for the human ear, first developed by Fletcher & Munson in 1933, show a difference in loudness level of 18 db for the two frequencies. Thus the ear is about 18 db more sensitive at the image frequency produced by the sampling process described in the above-identified patents than at the fundamental frequency. Thus instead of having an effective attenuation of -29.8 db, because of ear sensitivity, this is reduced at about -11.8 db. Even if the number of data samples was increased from 32 points to 64 points, as provided in the polyphonic tone systhesizer described in the above-identified copending application thereby doubling the image frequency because of ear sensitivity, the effective attenuation still is no greater than -16 db which is insufficient to prevent the unwanted image frequency from being noticeably heard.
One obvious solution to the reduction of sounds that the image frequencies produce by the sampling process is to use low-pass filters following the digital-to-analog conversion. Such an arrangement is only possible if each tone is generated through an independent channel. Even so, the cutoff frequency of the filter would have to change with the fundamental frequency of the note being generated. Low-pass filters cannot be used at all in the digital organ described in the U.S. Pat. No. 3,515,792, for example, where a time multiplexing is used so that the tone generator shares common digital channels and a single output digital-to-analog conversion channel.